Starting with just a multiplication board, some acetate strips (cut from different colored report covers), or colored counters you can bring the “magic” alive to help students with problem solving.

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Finding Equivalent FractionsNumbers on the board form equivalent fractions whether the numerator is directly on top of the denominator or the numerator and denominator are separate.

Take ½ for example (marked by red circles). As you read across the board horizontally, note that each fraction from L to R is equal to ½. ½ = {2/4,

3/6, . . . 12/24}.

Take 4/7 for example (marked by purple circles). As you read across the board

horizontally, note that each fraction from L to R is equal to 4/7. 4/7 = {8/14,

12/21, . . . 48/84}.

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Adding and Subtracting Unlike FractionsHere is a different approach for students who are having problems adding and subtracting fractions with unlike denominators. Before you begin, ensure students know the difference between “like” and “unlike” fractions and understand “common multiples” and “least common denominator” (LCD).

Step 1 - Finding the LCDFor example: When adding 1/7 + 2/5. Place one of the acetate strips over the 5s row and the other over the 7s row.

Beginning with the greater number “7”, cross-reference the multiples in each row until you find the lowest matching multiple. This will be the least common multiple or LCD; in this case, “35”.

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Adding and Subtracting Unlike FractionsNow we must convert 1/7 and 2/5 to equivalent fractions each with a denominator of 35.

Step 2 – Convert the first fraction 1/7 Starting with 1/7, Place on colored acetate strip over the 1s row and the other over the 7s row. Equivalent fractions for 1/7 are now highlighted on the table. Move along the denominator (7s) row until you come to the LCD, “35”. Now move up this column until you reach the highlighted number in the 1s row which is “5”. By doing this you show that 1/7 = 5/35.

X 1 2 3 4 5 6 7 8 9 10 11 121 1 2 3 4 5 6 7 8 9 10 11 122 2 4 6 8 10 12 14 16 18 20 22 243 3 6 9 12 15 18 21 24 27 30 33 364 4 8 12 16 20 24 28 32 36 40 44 485 5 10 15 20 25 30 35 40 45 50 55 606 6 12 18 24 30 36 42 48 54 60 66 727 7 14 21 28 35 42 49 56 63 70 77 848 8 16 24 32 40 48 56 64 72 80 88 969 9 18 27 36 45 54 63 72 81 90 99 10810 10 20 30 40 50 60 70 80 80 10

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Adding and Subtracting Unlike FractionsNow we must convert 1/7 and 2/5 to equivalent fractions each with a denominator of 35.

Step 3 – Convert the second fraction 2/5

Now follow the same steps for 2/5. Place on colored acetate strip over the 2s row and the other over the 5s row. Equivalent fractions for 2/5 are now highlighted on the table. Move along the denominator row (5s) until you come to the LCD, “35”. Now move up this column until you reach the highlighted number in the 2s row which is “14”. By doing this you show that 2/5 = 14/35.

Adding and Subtracting Unlike Fractions

Step 4 – Add (or subtract) the like fractions1/7 + 2/5 = 5/35 + 14/35 = 19/35

Resources Forsten, C. (2005). Math Strategies You Can Count On: Tools & Activities to build Math Appreciation, Understanding & Skills. Peterborough , NH: Crystal Springs Books.

Kohfeldt, Joyce. Innovative Educational Support Systems. 2008. 2 November 2008 <http://www.iessstore.com/conferences/2008-10-30SMC.php>.